Two effective heuristic methods of determining the numbers of fuzzy clustering centers based on bilevel programming

Fuzzy clustering method plays an increasingly important role in data analysis, image segmentation and many other fields. How to determine the number of clustering centers is a technical problem faced by most clustering methods. Starting from the index-based clustering method and the idea based on the fusion of multiple clustering techniques, this paper designs two methods of determining the numbers of fuzzy clustering centers based on bilevel programming respectively. Firstly, based on the bilevel fuzzy clustering model, an evolutionary algorithm is designed based on the absorptive criterion of fuzzy clustering method(EA-Ac-FCM), and its effectiveness in solving bilevel fuzzy clustering problem is verified by empirical analysis. Secondly, we propose an alternate minimization clustering by a collaborative strategy(AM-CC), the mean shift and fuzzy clustering complement each other and guide the clustering together. Compared with the traditional clustering methods, all of the numerical tests show that the two proposed methods could identify the number of cluster centers of the objective to be clustered correctly and handle the data analysis and image segmentation tasks better. •The technology of merging cluster centers one by one is regarded as mutation operators in evolutionary optimization process.•The possibility of cooperative optimization based on bilevel programming model is discussed for the first time.•The proposed AM-CC algorithm could perform the task of instance segmentation and panoramic segmentation.